Hi Mike,
Can you explain this Q #29 from Calculator section of Oct 2022 PSAT:

A quadratic function can be used to model the height, in feet, of an object above the ground in terms of time, in seconds, after the object was launched. According to the model, an object was launched into the air from a height of 0 feet and reached its maximum height of 3136 feet 14 seconds after it was launched. Based on the model, what was the height, in feet, of the object 1 second after it was launched?

Sure thing. The key here is recognizing early what the question is really testing, which is your knowledge of the vertex form of a parabola: y=a(x-h)^2+k, where (h, k) is the vertex.

The question tells us the object reaches a height of 3136 feet at 14 seconds, so the vertex of this parabola is at (14, 3136). Therefore, the equation of the parabola is y=a(x-14)^2+3136.

We also know from the question that the object is at (0,0) when it launches, and we can use that to solve for a:


Now we’re ready to figure out the object’s height when x=1.


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